309 research outputs found
The Zero-Undetected-Error Capacity Approaches the Sperner Capacity
Ahlswede, Cai, and Zhang proved that, in the noise-free limit, the
zero-undetected-error capacity is lower bounded by the Sperner capacity of the
channel graph, and they conjectured equality. Here we derive an upper bound
that proves the conjecture.Comment: 8 Pages; added a section on the definition of Sperner capacity;
accepted for publication in the IEEE Transactions on Information Theor
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
Comparison of Polar Decoders with Existing Low-Density Parity-Check and Turbo Decoders
Polar codes are a recently proposed family of provably capacity-achieving
error-correction codes that received a lot of attention. While their
theoretical properties render them interesting, their practicality compared to
other types of codes has not been thoroughly studied. Towards this end, in this
paper, we perform a comparison of polar decoders against LDPC and Turbo
decoders that are used in existing communications standards. More specifically,
we compare both the error-correction performance and the hardware efficiency of
the corresponding hardware implementations. This comparison enables us to
identify applications where polar codes are superior to existing
error-correction coding solutions as well as to determine the most promising
research direction in terms of the hardware implementation of polar decoders.Comment: Fixes small mistakes from the paper to appear in the proceedings of
IEEE WCNC 2017. Results were presented in the "Polar Coding in Wireless
Communications: Theory and Implementation" Worksho
Lengthening and Extending Binary Private Information Retrieval Codes
It was recently shown by Fazeli et al. that the storage overhead of a
traditional -server private information retrieval (PIR) protocol can be
significantly reduced using the concept of a -server PIR code. In this work,
we show that a family of -server PIR codes (with increasing dimensions and
blocklengths) can be constructed from an existing -server PIR code through
lengthening by a single information symbol and code extension by at most
code symbols. Furthermore, by extending a code
construction notion from Steiner systems by Fazeli et al., we obtain a specific
family of -server PIR codes. Based on a code construction technique that
lengthens and extends a -server PIR code simultaneously, a basic algorithm
to find good (i.e., small blocklength) -server PIR codes is proposed. For
the special case of , we find provably optimal PIR codes for code
dimensions , while for all we find codes of smaller
blocklength than the best known codes from the literature. Furthermore, in the
case of , we also find better codes for . Numerical
results show that most of the best found -server PIR codes can be
constructed from the proposed family of codes connected to Steiner systems.Comment: The shorter version of this paper will appear in the proceedings of
2018 International Zurich Seminar on Information and Communicatio
Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?
We present nonasymptotic upper and lower bounds on the maximum coding rate
achievable when transmitting short packets over a Rician memoryless
block-fading channel for a given requirement on the packet error probability.
We focus on the practically relevant scenario in which there is no \emph{a
priori} channel state information available at the transmitter and at the
receiver. An upper bound built upon the min-max converse is compared to two
lower bounds: the first one relies on a noncoherent transmission strategy in
which the fading channel is not estimated explicitly at the receiver; the
second one employs pilot-assisted transmission (PAT) followed by
maximum-likelihood channel estimation and scaled mismatched nearest-neighbor
decoding at the receiver. Our bounds are tight enough to unveil the optimum
number of diversity branches that a packet should span so that the energy per
bit required to achieve a target packet error probability is minimized, for a
given constraint on the code rate and the packet size. Furthermore, the bounds
reveal that noncoherent transmission is more energy efficient than PAT, even
when the number of pilot symbols and their power is optimized. For example, for
the case when a coded packet of symbols is transmitted using a channel
code of rate bits/channel use, over a block-fading channel with block
size equal to symbols, PAT requires an additional dB of energy per
information bit to achieve a packet error probability of compared to
a suitably designed noncoherent transmission scheme. Finally, we devise a PAT
scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics
decoding, whose performance are close ( dB gap at packet error
probability) to the ones predicted by our PAT lower bound. This shows that the
PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa
Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation
In this work, we present a concatenated repetition-polar coding scheme that
is aimed at applications requiring highly unbalanced unequal bit-error
protection, such as the Beam Interlock System of the Large Hadron Collider at
CERN. Even though this concatenation scheme is simple, it reveals significant
challenges that may be encountered when designing a concatenated scheme that
uses a polar code as an inner code, such as error correlation and unusual
decision log-likelihood ratio distributions. We explain and analyze these
challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and
Computers, November 201
Blind Detection of Polar Codes
Polar codes were recently chosen to protect the control channel information
in the next-generation mobile communication standard (5G) defined by the 3GPP.
As a result, receivers will have to implement blind detection of polar coded
frames in order to keep complexity, latency, and power consumption tractable.
As a newly proposed class of block codes, the problem of polar-code blind
detection has received very little attention. In this work, we propose a
low-complexity blind-detection algorithm for polar-encoded frames. We base this
algorithm on a novel detection metric with update rules that leverage the a
priori knowledge of the frozen-bit locations, exploiting the inherent
structures that these locations impose on a polar-encoded block of data. We
show that the proposed detection metric allows to clearly distinguish
polar-encoded frames from other types of data by considering the cumulative
distribution functions of the detection metric, and the receiver operating
characteristic. The presented results are tailored to the 5G standardization
effort discussions, i.e., we consider a short low-rate polar code concatenated
with a CRC.Comment: 6 pages, 8 figures, to appear at the IEEE Int. Workshop on Signal
Process. Syst. (SiPS) 201
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